// Numbas version: exam_results_page_options {"name": "Scientific notation: large numbers to scientific notation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": ["converting", "scientific notation", "standard form"], "ungrouped_variables": ["dec1", "pow1", "q1", "dec2", "pow2", "q2"], "advice": "", "parts": [{"scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "steps": [{"scripts": {}, "type": "information", "unitTests": [], "showFeedbackIcon": true, "prompt": "

A number is in scientific notation if it is written as a decimal multiplied by some power of 10, where the decimal has exactly one digit in front of the decimal place. For example:

\n

\$1.234\\times 10^6, \\quad \\text{and} \\quad 3.01\\times 10^{-3}\$

\n

are both in scientific notation.

\n

\n
\n

Suppose we have the number $\\var{q1}$. In scientific notation, this number would start with $\\var{dec1}$ since we only want one digit in front of the decimal point. The decimal point is currently to the right of the last digit in $\\var{q1}$ and needs to move to between the first and second digits, that is $\\var{dec1}$. Count the places that the decimal point must jump and you get $\\var{pow1}$ places. That is,

\n

\n

\$\\var{q1}=\\var{dec1}\\times 10^{\\var{pow1}}\$

\n

\n

We have a positive $\\var{pow1}$ as the power because we need to make the number $\\var{dec1}$ bigger to get to $\\var{q1}$.

", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "marks": 0}], "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "prompt": "

$\\var{q1} =$ [[0]]$\\times 10$ [[1]]

", "extendBaseMarkingAlgorithm": true, "gaps": [{"scripts": {}, "type": "numberentry", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "maxValue": "{dec1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "minValue": "{dec1}", "showCorrectAnswer": false, "mustBeReduced": false, "unitTests": [], "showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "marks": "0.5"}, {"scripts": {}, "type": "numberentry", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "maxValue": "{pow1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "minValue": "{pow1}", "showCorrectAnswer": false, "mustBeReduced": false, "unitTests": [], "showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "marks": "0.5"}], "variableReplacements": [], "sortAnswers": false, "marks": 0}, {"scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "steps": [{"scripts": {}, "type": "information", "unitTests": [], "showFeedbackIcon": true, "prompt": "

A number is in scientific notation if it is written as a decimal multiplied by some power of 10, where the decimal has exactly one digit in front of the decimal place. For example:

\n

\$1.234\\times 10^6, \\quad \\text{and} \\quad 3.01\\times 10^{-3}\$

\n

are both in scientific notation.

\n

\n
\n

Suppose we have the number $\\var{q2}$. In scientific notation, this number would start with $\\var{dec2}$ since we only want one digit in front of the decimal point. The decimal point is currently to the right of the last digit in $\\var{q2}$ and needs to move to between the first and second digits, that is $\\var{dec2}$. Count the places that the decimal point must jump and you get $\\var{pow2}$ places. That is,

\n

\n

\$\\var{q2}=\\var{dec2}\\times 10^{\\var{pow2}}\$

\n

\n

We have a positive $\\var{pow2}$ as the power because we need to make the number $\\var{dec2}$ bigger to get to $\\var{q2}$.

", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "marks": 0}], "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "customMarkingAlgorithm": "", "prompt": "

$\\var{q2} =$ [[0]]$\\times 10$ [[1]]

", "extendBaseMarkingAlgorithm": true, "gaps": [{"scripts": {}, "type": "numberentry", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "maxValue": "{dec2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "minValue": "{dec2}", "showCorrectAnswer": false, "mustBeReduced": false, "unitTests": [], "showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "marks": "0.5"}, {"scripts": {}, "type": "numberentry", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "maxValue": "{pow2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "minValue": "{pow2}", "showCorrectAnswer": false, "mustBeReduced": false, "unitTests": [], "showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "marks": "0.5"}], "variableReplacements": [], "sortAnswers": false, "marks": 0}], "statement": "

If you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.

\n

\n

Write the following numbers in scientific notation.

", "rulesets": {}, "functions": {"spacenumber": {"language": "javascript", "type": "string", "definition": "var parts=n.toString().split(\".\");\n if(parts[1] && parts[1].length<2) {\n parts[1]+='0';\n }\n return parts[0].replace(/\\B(?=(\\d{3})+(?!\\d))/g, \" \") + (parts[1] ? \", \" + parts[1] : \"\");", "parameters": [["n", "number"]]}}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [], "extensions": [], "variables": {"pow2": {"definition": "random(4..8)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "pow2"}, "pow1": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "pow1"}, "q2": {"definition": "precround(dec2*10^pow2,0)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "q2"}, "q1": {"definition": "precround(dec1*10^pow1,0)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "q1"}, "dec2": {"definition": "random(1.1..9.9#0.001)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "dec2"}, "dec1": {"definition": "random(1.1..9.9#0.01)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "dec1"}}, "name": "Scientific notation: large numbers to scientific notation", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}